Since TDs are singularities in the field of the eigenvector, it can be expected that they are directly related with the heterogeneous mechanical response of the system under shear. To explore this connection we have determined the plastic instabilities of the sample if it is put under an athermal quasi-static pure shear, see Methods for details. For a sheared configuration at strain \(\gamma \)  we calculate \(D^2_{\rm min}\) , the field of non-affine displacement of the particles between two consecutive configurations (having a difference in strain of 0.05%) [1]}. After a drop in the stress, signaling that a plastic event has occurred, we identify the particles that have a high \(D^2_{\rm min}\)  (top 5%, see Extended Data Fig. REF ), and associate these particles to a PE.
The location of these PEs can be correlated with the position of the TDs by means of a corresponding radial distribution function \(g_{\alpha \rm PE}(r)\) ,
where \(\alpha \in \lbrace \pm 1\rbrace \) . In Fig.  REF(a)-(b) we show the resulting correlation for different values of \(\omega \)  and one recognizes that \(g_{+ \rm PE}(r)\)  is basically flat, implying that there is only very little correlation of the PE with the positive TDs, and this holds for all frequencies. The only noticeable feature in the curve is the small peak at around \(r=2\)  if \(\omega \)  is small, the origin of which is discussed below.
